Preprint 2002-020

Undercompressive Shock Waves and the Dafermos Regularization

Stephen Schecter

Abstract:
For a system of conservation laws in one space dimension, we identify all
structurally stable Riemann solutions that include only shock waves. Shock
waves are required to satisfy the viscous profile criterion for a given
viscosity $(B(u)u_ x)_x$. Undercompressive shock waves are allowed. We also
show that all such Riemann solutions have nearby smooth solutions of the
Dafermos regularization with the given viscosity.